JEE Main 2020 January 8 Shift 1 Question Paper & Solutions - JEE MCQ

A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed ω about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is

Boolean relation at the output stage-Y for the following circuit is:

Consider a solid sphere of radius R and mass density  The minimum density of a liquid in which it will float is:

Proton with kinetic energy of 1 MeV moves from south to north. It gets an acceleration of 10¹² m/s² by an applied magnetic field (west to east). The value of magnetic field is:
(Rest mass of proton is 1.6 × 10^-27 kg)

The dimension of stopping potential V₀ in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant 'G' and ampere A is:

A thermodynamic cycle xyzx is shown on a V-T diagram.

The P-V diagram that best describes this cycle is: (Diagrams are schematic and not to scale.)

Consider two solid spheres of radii R₁ = 1 m, R₂ = 2 m and masses M₁ and M₂, respectively. The gravitational field due to sphere (1) and (2) is shown. The value of M₁/M₂ is

The plot that depicts the behaviour of the mean free time τ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale.)

The graph which depicts the results of Rutherford gold foil experiment with α-particle is:
θ: Scattering angle
Y: Number of scattered α-particles detected
(Plots are schematic and not to scale.)

Three charged particles A, B and C with charges -4q, 2q and -2q are present on the circumference of a circle of radius d. The charged particles A, C and centre O of the circle formed an equilateral triangle as shown in figure. Electric field at O along x-direction is

In finding the electric field using Gauss law, the formula   is applicable. In the formula, ε₀ is permittivity of free space, A is the area of Gaussian surface and qenc is charge enclosed by the Gaussian surface. This equation can be used in which of the following situations?

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4 kg (The coordinates of the same are shown in figure) are

At time t = 0, magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next 5 s, then induced EMF in the loop is

The critical angle of medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability 4/3 for this wavelength, will be

The magnifying power of a telescope with tube length 60 cm is 5. What is the focal length of its eye-piece?

Consider a uniform rod of mass M = 4 m and length l pivoted about its centre. A mass m moving with velocity v making angle θ = π/4 to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is

A leak proof cylinder of length 1 m, made of a metal which has very low coefficient of expansion, is floating vertically in water at 0°C such that its height above the water surface is 20 cm. When the temperature of water is increased to 4°C, the height of the cylinder above the water surface becomes 21 cm. The density of water at T = 4°C relative to the density at T = 0°C is close to? (Answer upto 2 decimal places)

Four resistances of 15 Ω, 12 Ω, 4 Ω and 10 Ω respectively in cyclic order to form Wheatstone's network. The resistance that is to be connected in parallel with the resistance of 10 Ω to balance the network is _________ Ω.

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP in 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.

A body A of mass m = 0.1 kg has an initial velocity of . It collides elastically with another body B of the same mass which has an initial velocity of . After collision, A moves with a velocity  The energy of B after collision is written as x/10 J. The value of x is ______.(Nearest Integer)

A particle is moving along the x-axis with its coordinate with time 't' given by x(t) = 10 + 8t - 3t². Another particle is moving along the y-axis with its coordinate as a function of time given by y(t) = 5 - 8t³. At t = 1 s, the speed of the second particle as measured in the frame of the first particle is given as √v. Then v (in m/s) is _______.(Nearest Integer)

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is 30 cm and the refractive index of the lens material is 1.5, then the focal length of the lens (in cm) is _______.

The complex that can show fac-and mer-isomers is

As per Hardy-Schulze formulation, the flocculation values of the following for ferric hydroxide sol are in the order:

The decreasing order of reactivity towards dehydrohalogenation (E₁) reaction of the following compounds is

For the Balmer series in the spectrum of H atom,  the correct statements among (l) to (IV) are:
(I) As wavelength decreases, the lines in the series converge.
(II) The integer n₁ is equal to 2.
(III) The lines of longest wavelength correspond to n₂ = 3.
(IV) The ionisation energy of hydrogen can be calculated from wave number of these lines.

The first ionisation energy (in kJ/mol) of Na, Mg, Al and Si, respectively, is: